1. 3.6 Graph Rational Functions Part II

2. Remember Rational functions have asymptotes To find the vertical asymptote, set the denominator = 0 and solve for x x-5 = 0 x=5

3. To find horizontal asymptote Eliminate any term that involves an x and solve for y y = 3

4. Using Asymptotes to Graph Draw dotted lines for asymptotes Pick values for x based on the asymptotes and solve for y

5. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the function and identify its domain and range. Compare the graph with the graph of y = 1 x ANSWER 1. y = – 4 x Domain: all real numbers except 0 Range: all real numbers except 0 The graph is a vertical stretch of y = that is then reflected in the x -axis. 1 x

6. GUIDED PRACTICE for Examples 1, 2 and 3 2. y = 1 x – 4 1 x Domain: all real numbers except 0 Range: all real numbers except – 4 The graph is a vertical translation (of 4 units down) of the graph y =. ANSWER Graph the function and identify its domain and range. Compare the graph with the graph of y = 1 x

7. GUIDED PRACTICE for Examples 1, 2 and 3 3. y = 1 x + 5 1 x Domain: all real numbers except – 5 Range: all real numbers except 0 The graph is a horizontal translation (of 5 units left) of the graph y =. Graph the function and identify its domain and range. Compare the graph with the graph of y = 1 x ANSWER

8. GUIDED PRACTICE for Examples 1, 2 and 3 y = 1 x + 3 4. Describe how the graph of is related to the graph of y =. 1 x The graph of y = is a horizontal translation (of 3 units left) of the graph of y =. x + 3 1 x 1 ANSWER

9. SOLUTION EXAMPLE 4 Graph y = + k a x – h Graph y = – 3. 2 x + 1

10. GUIDED PRACTICE for Example 4 5. Graph y = + 6 4 x – 5 ANSWER

11. GUIDED PRACTICE for Example 4 6. For which function is the domain all real numbers except –3 and the range all real numbers except 7 ? A. y = + 7. 2 x – 3 B. y = – 7. 2 x – 3 C. y = + 7. 2 x + 3 D. y = – 7. 2 x + 3 ANSWER C. y = + 7. 2 x + 3